Morphisms on infinite alphabets, countable states automata and regular sequences

Jie-Meng Zhang, Jin Chen, Yingjun Guo, Zhixiong Wen

In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings.

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